Localization in an imaginary vector potential

Abstract

Eigenfunctions of 1d disordered Hamiltonian with constant imaginary vector potential are investigated. Even within the domain of complex eigenvalues the wave functions are shown to be strongly localized. However, this localization is of a very unusual kind. The logarithm of the wave function at different coordinates $x$ fluctuates strongly (just like the position of Brownian particle fluctuates in time). After approaching its maximal value the logarithm decreases like the square root of the distance $\overline{(\ln |{\psi }_{max}/\psi |{)}^2}\sim |x-x_0|$. The extension of the model to the quasi-1d case is also considered.

4 pages, REVTEX, 2 eps figures. Discussion of physical applications extended. References added

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• Erratic non-Hermitian skin localization
• Delocalization in an open one-dimensional chain in an imaginary vector potential
• Tight-binding lattices with an oscillating imaginary gauge field
• Modulational Instability and Dynamical Growth Blockade in the Nonlinear Hatano-Nelson Model
• Vortices in a cylinder: Localization after depinning
• Two-dimensional Non-Hermitian Delocalization Transition as a Probe for the Localization Length
• "Lifshitz tails" and extended states in an Imaginary random potential
• Reconfiguration of quantum states in $\mathcal{P}T$-symmetric quasi-one dimensional lattices
• Phase transitions in non-Hermitian superlattices
• Theory of Localization in a Disordered Ring in a Non-Hermitian Field
• Non-hermitean delocalization in an array of wells with variable-range widths